MinT - Best Known (177−51, 177, s)-Nets in Base 4

Best Known (177−51, 177, s)-Nets in Base 4

(177−51, 177, 531)-Net over F₄ — Constructive and digital

Digital (126, 177, 531)-net over F₄, using

t-expansion [i] based on digital (125, 177, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 59, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(177−51, 177, 891)-Net over F₄ — Digital

Digital (126, 177, 891)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−51, 177, 58729)-Net in Base 4 — Upper bound on s

There is no (126, 177, 58730)-net in base 4, because

1 times m-reduction [i] would yield (126, 176, 58730)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9175 792068 745583 774694 016084 515292 551373 449304 328925 441379 002634 083384 535146 783319 259858 271279 922841 928106 > 4¹⁷⁶ [i]