MinT - Best Known (214−89, 214, s)-Nets in Base 4

Best Known (214−89, 214, s)-Nets in Base 4

(214−89, 214, 130)-Net over F₄ — Constructive and digital

Digital (125, 214, 130)-net over F₄, using

t-expansion [i] based on digital (105, 214, 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]

(214−89, 214, 274)-Net over F₄ — Digital

Digital (125, 214, 274)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−89, 214, 4688)-Net in Base 4 — Upper bound on s

There is no (125, 214, 4689)-net in base 4, because

1 times m-reduction [i] would yield (125, 213, 4689)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 174 848759 463699 884396 021409 731301 412339 384709 058564 478693 328531 402868 518012 873222 900802 566319 135543 471926 309056 787559 157874 533480 > 4²¹³ [i]