MinT - Best Known (230−105, 230, s)-Nets in Base 4

Best Known (230−105, 230, s)-Nets in Base 4

(230−105, 230, 130)-Net over F₄ — Constructive and digital

Digital (125, 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]

(230−105, 230, 217)-Net over F₄ — Digital

Digital (125, 230, 217)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−105, 230, 2978)-Net in Base 4 — Upper bound on s

There is no (125, 230, 2979)-net in base 4, because

1 times m-reduction [i] would yield (125, 229, 2979)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 751623 296949 481120 752143 139743 724979 348000 693859 903879 218564 932970 132788 453951 265474 246766 140769 112234 515648 322623 169692 343029 742960 795040 > 4²²⁹ [i]