MinT - Best Known (238−107, 238, s)-Nets in Base 4

Best Known (238−107, 238, s)-Nets in Base 4

(238−107, 238, 130)-Net over F₄ — Constructive and digital

Digital (131, 238, 130)-net over F₄, using

t-expansion [i] based on digital (105, 238, 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]

(238−107, 238, 234)-Net over F₄ — Digital

Digital (131, 238, 234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−107, 238, 3336)-Net in Base 4 — Upper bound on s

There is no (131, 238, 3337)-net in base 4, because

1 times m-reduction [i] would yield (131, 237, 3337)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49222 974303 822433 816303 807539 964070 744166 650341 387617 834809 084326 362775 389189 108339 723346 158976 164903 643129 248060 087182 981317 053479 851709 916160 > 4²³⁷ [i]