MinT - Best Known (122, 122+61, s)-Nets in Base 4

Best Known (122, 122+61, s)-Nets in Base 4

(122, 122+61, 195)-Net over F₄ — Constructive and digital

Digital (122, 183, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 61, 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]

(122, 122+61, 240)-Net in Base 4 — Constructive

(122, 183, 240)-net in base 4, using

1 times m-reduction [i] based on (122, 184, 240)-net in base 4, using
- trace code for nets [i] based on (30, 92, 120)-net in base 16, using
  - 3 times m-reduction [i] based on (30, 95, 120)-net in base 16, using
    - base change [i] based on digital (11, 76, 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]

(122, 122+61, 509)-Net over F₄ — Digital

Digital (122, 183, 509)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 122+61, 18012)-Net in Base 4 — Upper bound on s

There is no (122, 183, 18013)-net in base 4, because

1 times m-reduction [i] would yield (122, 182, 18013)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 606130 969974 011876 984402 616090 591295 683558 852496 469103 182592 319518 418444 779201 909961 032214 693728 231996 191760 > 4¹⁸² [i]