MinT - Best Known (99−31, 99, s)-Nets in Base 4

Best Known (99−31, 99, s)-Nets in Base 4

(99−31, 99, 240)-Net over F₄ — Constructive and digital

Digital (68, 99, 240)-net over F₄, using

t-expansion [i] based on digital (67, 99, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 33, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(99−31, 99, 401)-Net over F₄ — Digital

Digital (68, 99, 401)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−31, 99, 18357)-Net in Base 4 — Upper bound on s

There is no (68, 99, 18358)-net in base 4, because

1 times m-reduction [i] would yield (68, 98, 18358)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 100451 279641 147881 738672 128597 384445 861064 871738 192396 437528 > 4⁹⁸ [i]