MinT - Best Known (249−116, 249, s)-Nets in Base 4

Best Known (249−116, 249, s)-Nets in Base 4

(249−116, 249, 130)-Net over F₄ — Constructive and digital

Digital (133, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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]

(249−116, 249, 218)-Net over F₄ — Digital

Digital (133, 249, 218)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−116, 249, 2828)-Net in Base 4 — Upper bound on s

There is no (133, 249, 2829)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 824659 777496 964424 826961 252778 804991 279582 646241 930257 708680 998409 703690 244501 740276 894067 475857 189641 319256 011809 112563 057561 275648 782571 247662 557600 > 4²⁴⁹ [i]