MinT - Best Known (230−112, 230, s)-Nets in Base 4

Best Known (230−112, 230, s)-Nets in Base 4

(230−112, 230, 130)-Net over F₄ — Constructive and digital

Digital (118, 230, 130)-net over F₄, using

t-expansion [i] based on digital (105, 230, 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]

(230−112, 230, 177)-Net over F₄ — Digital

Digital (118, 230, 177)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−112, 230, 2103)-Net in Base 4 — Upper bound on s

There is no (118, 230, 2104)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 027756 563437 841065 099759 041356 017035 400070 829387 151181 749470 980122 989255 834164 490790 526862 345280 422093 907658 584991 838341 529989 682203 309152 > 4²³⁰ [i]