MinT - Best Known (247−113, 247, s)-Nets in Base 4

Best Known (247−113, 247, s)-Nets in Base 4

(247−113, 247, 130)-Net over F₄ — Constructive and digital

Digital (134, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 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]

(247−113, 247, 229)-Net over F₄ — Digital

Digital (134, 247, 229)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−113, 247, 3147)-Net in Base 4 — Upper bound on s

There is no (134, 247, 3148)-net in base 4, because

1 times m-reduction [i] would yield (134, 246, 3148)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12853 387621 041280 111828 300402 733546 692833 906215 479684 119571 504130 684428 802669 936428 516846 795496 286829 156366 396028 976980 911894 227298 641218 557075 382500 > 4²⁴⁶ [i]