MinT - Best Known (127, 127+105, s)-Nets in Base 4

Best Known (127, 127+105, s)-Nets in Base 4

(127, 127+105, 130)-Net over F₄ — Constructive and digital

Digital (127, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 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]

(127, 127+105, 224)-Net over F₄ — Digital

Digital (127, 232, 224)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+105, 3143)-Net in Base 4 — Upper bound on s

There is no (127, 232, 3144)-net in base 4, because

1 times m-reduction [i] would yield (127, 231, 3144)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 934199 965256 662831 156316 715578 071729 391515 333957 775992 079811 923614 606742 997668 252567 734796 201835 246663 234642 090930 220436 388883 912592 507300 > 4²³¹ [i]