MinT - Best Known (245−123, 245, s)-Nets in Base 4

Best Known (245−123, 245, s)-Nets in Base 4

(245−123, 245, 130)-Net over F₄ — Constructive and digital

Digital (122, 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]

(245−123, 245, 170)-Net over F₄ — Digital

Digital (122, 245, 170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−123, 245, 1960)-Net in Base 4 — Upper bound on s

There is no (122, 245, 1961)-net in base 4, because

1 times m-reduction [i] would yield (122, 244, 1961)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 803 822829 351304 228172 012384 376459 454333 516152 651853 024425 012460 681621 209543 142544 815488 346524 266079 128152 201823 632933 869841 775793 401703 077173 292800 > 4²⁴⁴ [i]