MinT - Best Known (77, 228, s)-Nets in Base 4

Best Known (77, 228, s)-Nets in Base 4

(77, 228, 104)-Net over F₄ — Constructive and digital

Digital (77, 228, 104)-net over F₄, using

t-expansion [i] based on digital (73, 228, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(77, 228, 112)-Net over F₄ — Digital

Digital (77, 228, 112)-net over F₄, using

t-expansion [i] based on digital (73, 228, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(77, 228, 576)-Net in Base 4 — Upper bound on s

There is no (77, 228, 577)-net in base 4, because

1 times m-reduction [i] would yield (77, 227, 577)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48992 204175 807395 276734 232145 359397 911021 840579 181167 494996 446883 924725 682537 608161 633975 695365 481668 090941 462191 671901 587200 996235 023872 > 4²²⁷ [i]