MinT - Best Known (119, 119+113, s)-Nets in Base 4

Best Known (119, 119+113, s)-Nets in Base 4

(119, 119+113, 130)-Net over F₄ — Constructive and digital

Digital (119, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(119, 119+113, 178)-Net over F₄ — Digital

Digital (119, 232, 178)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+113, 2157)-Net in Base 4 — Upper bound on s

There is no (119, 232, 2158)-net in base 4, because

1 times m-reduction [i] would yield (119, 231, 2158)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 149941 078246 428519 587963 891786 569225 907920 913689 930665 709389 667675 899484 049139 749487 602484 302904 377392 995196 445582 774227 977637 500517 009900 > 4²³¹ [i]