MinT - Best Known (241−107, 241, s)-Nets in Base 4

Best Known (241−107, 241, s)-Nets in Base 4

(241−107, 241, 130)-Net over F₄ — Constructive and digital

Digital (134, 241, 130)-net over F₄, using

t-expansion [i] based on digital (105, 241, 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]

(241−107, 241, 246)-Net over F₄ — Digital

Digital (134, 241, 246)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−107, 241, 3612)-Net in Base 4 — Upper bound on s

There is no (134, 241, 3613)-net in base 4, because

1 times m-reduction [i] would yield (134, 240, 3613)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 153401 625313 522324 823787 084532 266067 902920 090875 270672 075367 281092 593984 312625 427154 952251 841709 083621 182476 518489 430440 889166 154122 708354 935360 > 4²⁴⁰ [i]