MinT - Best Known (180−75, 180, s)-Nets in Base 4

Best Known (180−75, 180, s)-Nets in Base 4

(180−75, 180, 130)-Net over F₄ — Constructive and digital

Digital (105, 180, 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]

(180−75, 180, 234)-Net over F₄ — Digital

Digital (105, 180, 234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−75, 180, 3964)-Net in Base 4 — Upper bound on s

There is no (105, 180, 3965)-net in base 4, because

1 times m-reduction [i] would yield (105, 179, 3965)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 591367 319483 997065 385778 599031 416567 104587 636878 995645 702763 350062 571474 839307 288279 875951 902712 332531 197284 > 4¹⁷⁹ [i]