MinT - Best Known (77, 77+149, s)-Nets in Base 4

Best Known (77, 77+149, s)-Nets in Base 4

(77, 77+149, 104)-Net over F₄ — Constructive and digital

Digital (77, 226, 104)-net over F₄, using

t-expansion [i] based on digital (73, 226, 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, 77+149, 112)-Net over F₄ — Digital

Digital (77, 226, 112)-net over F₄, using

t-expansion [i] based on digital (73, 226, 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, 77+149, 581)-Net in Base 4 — Upper bound on s

There is no (77, 226, 582)-net in base 4, because

1 times m-reduction [i] would yield (77, 225, 582)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3141 849400 697299 322496 781613 416160 497118 679166 268945 440924 368444 437178 167753 399798 323606 255476 850521 355614 095517 838841 095064 516147 355520 > 4²²⁵ [i]