MinT - Best Known (113, 113+103, s)-Nets in Base 4

Best Known (113, 113+103, s)-Nets in Base 4

(113, 113+103, 130)-Net over F₄ — Constructive and digital

Digital (113, 216, 130)-net over F₄, using

t-expansion [i] based on digital (105, 216, 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]

(113, 113+103, 179)-Net over F₄ — Digital

Digital (113, 216, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+103, 2242)-Net in Base 4 — Upper bound on s

There is no (113, 216, 2243)-net in base 4, because

1 times m-reduction [i] would yield (113, 215, 2243)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2772 678677 541227 215811 095010 449247 312686 612987 026987 214558 946827 879583 761571 813150 539538 563749 003282 877231 581473 635334 434761 552880 > 4²¹⁵ [i]