MinT - Best Known (130, 130+65, s)-Nets in Base 4

Best Known (130, 130+65, s)-Nets in Base 4

(130, 130+65, 195)-Net over F₄ — Constructive and digital

Digital (130, 195, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 65, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(130, 130+65, 240)-Net in Base 4 — Constructive

(130, 195, 240)-net in base 4, using

3 times m-reduction [i] based on (130, 198, 240)-net in base 4, using
- trace code for nets [i] based on (31, 99, 120)-net in base 16, using
  - 1 times m-reduction [i] based on (31, 100, 120)-net in base 16, using
    - base change [i] based on digital (11, 80, 120)-net over F₃₂, using
      - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(130, 130+65, 538)-Net over F₄ — Digital

Digital (130, 195, 538)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+65, 19017)-Net in Base 4 — Upper bound on s

There is no (130, 195, 19018)-net in base 4, because

1 times m-reduction [i] would yield (130, 194, 19018)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 631 075740 499724 950677 926431 194645 576462 873866 682139 583338 244586 352735 119798 217488 873336 268318 154151 994443 147223 447966 > 4¹⁹⁴ [i]