MinT - Best Known (212−89, 212, s)-Nets in Base 4

Best Known (212−89, 212, s)-Nets in Base 4

(212−89, 212, 130)-Net over F₄ — Constructive and digital

Digital (123, 212, 130)-net over F₄, using

t-expansion [i] based on digital (105, 212, 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]

(212−89, 212, 263)-Net over F₄ — Digital

Digital (123, 212, 263)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−89, 212, 4399)-Net in Base 4 — Upper bound on s

There is no (123, 212, 4400)-net in base 4, because

1 times m-reduction [i] would yield (123, 211, 4400)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 879201 420134 741086 822363 139254 129763 699366 722591 571100 408899 594794 329685 119420 128419 496649 356368 996906 215046 879737 706784 202399 > 4²¹¹ [i]