MinT - Best Known (245−109, 245, s)-Nets in Base 4

Best Known (245−109, 245, s)-Nets in Base 4

(245−109, 245, 130)-Net over F₄ — Constructive and digital

Digital (136, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 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]

(245−109, 245, 248)-Net over F₄ — Digital

Digital (136, 245, 248)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−109, 245, 3627)-Net in Base 4 — Upper bound on s

There is no (136, 245, 3628)-net in base 4, because

1 times m-reduction [i] would yield (136, 244, 3628)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 808 832476 582987 073591 731876 512896 722878 019235 786153 639123 426338 991189 309036 404999 125171 786009 011025 410297 139407 059666 206034 881901 527974 058100 108096 > 4²⁴⁴ [i]