MinT - Best Known (231−103, 231, s)-Nets in Base 4

Best Known (231−103, 231, s)-Nets in Base 4

(231−103, 231, 130)-Net over F₄ — Constructive and digital

Digital (128, 231, 130)-net over F₄, using

t-expansion [i] based on digital (105, 231, 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]

(231−103, 231, 234)-Net over F₄ — Digital

Digital (128, 231, 234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−103, 231, 3393)-Net in Base 4 — Upper bound on s

There is no (128, 231, 3394)-net in base 4, because

1 times m-reduction [i] would yield (128, 230, 3394)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 019894 204524 724495 291895 672289 462801 014967 917115 955145 208975 279555 866051 414494 835849 865644 852127 347531 674456 023310 859656 707129 909788 417248 > 4²³⁰ [i]