MinT - Best Known (235−105, 235, s)-Nets in Base 4

Best Known (235−105, 235, s)-Nets in Base 4

(235−105, 235, 130)-Net over F₄ — Constructive and digital

Digital (130, 235, 130)-net over F₄, using

t-expansion [i] based on digital (105, 235, 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]

(235−105, 235, 236)-Net over F₄ — Digital

Digital (130, 235, 236)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−105, 235, 3409)-Net in Base 4 — Upper bound on s

There is no (130, 235, 3410)-net in base 4, because

1 times m-reduction [i] would yield (130, 234, 3410)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 771 734553 010196 045532 656384 700229 343713 724253 054343 724225 690659 099483 384130 161017 012816 390666 544035 883125 135871 523896 341871 286104 405173 711280 > 4²³⁴ [i]