MinT - Best Known (77, 77+174, s)-Nets in Base 4

Best Known (77, 77+174, s)-Nets in Base 4

(77, 77+174, 104)-Net over F₄ — Constructive and digital

Digital (77, 251, 104)-net over F₄, using

t-expansion [i] based on digital (73, 251, 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+174, 112)-Net over F₄ — Digital

Digital (77, 251, 112)-net over F₄, using

t-expansion [i] based on digital (73, 251, 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+174, 534)-Net in Base 4 — Upper bound on s

There is no (77, 251, 535)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 514884 578460 382935 816019 751382 493484 537167 309135 266738 937214 192091 907011 922325 523189 725083 107006 486485 807042 975152 879030 932395 187870 756159 658495 620000 > 4²⁵¹ [i]