MinT - Best Known (107, 107+89, s)-Nets in Base 4

Best Known (107, 107+89, s)-Nets in Base 4

(107, 107+89, 130)-Net over F₄ — Constructive and digital

Digital (107, 196, 130)-net over F₄, using

t-expansion [i] based on digital (105, 196, 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]

(107, 107+89, 191)-Net over F₄ — Digital

Digital (107, 196, 191)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+89, 2643)-Net in Base 4 — Upper bound on s

There is no (107, 196, 2644)-net in base 4, because

1 times m-reduction [i] would yield (107, 195, 2644)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2549 949989 668349 599212 675651 502636 000727 962620 497588 889994 045436 376160 039972 693603 058824 444034 988994 955975 082243 404152 > 4¹⁹⁵ [i]