MinT - Best Known (77, 77+78, s)-Nets in Base 4

Best Known (77, 77+78, s)-Nets in Base 4

(77, 77+78, 104)-Net over F₄ — Constructive and digital

Digital (77, 155, 104)-net over F₄, using

t-expansion [i] based on digital (73, 155, 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+78, 113)-Net over F₄ — Digital

Digital (77, 155, 113)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+78, 1236)-Net in Base 4 — Upper bound on s

There is no (77, 155, 1237)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2133 391016 767006 241143 693622 948502 015770 870721 174152 368195 685653 546480 369797 790862 736309 716512 > 4¹⁵⁵ [i]