MinT - Best Known (109, 109+89, s)-Nets in Base 4

Best Known (109, 109+89, s)-Nets in Base 4

(109, 109+89, 130)-Net over F₄ — Constructive and digital

Digital (109, 198, 130)-net over F₄, using

t-expansion [i] based on digital (105, 198, 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]

(109, 109+89, 199)-Net over F₄ — Digital

Digital (109, 198, 199)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+89, 2817)-Net in Base 4 — Upper bound on s

There is no (109, 198, 2818)-net in base 4, because

1 times m-reduction [i] would yield (109, 197, 2818)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40612 418803 017102 977316 354903 851398 121332 754198 580137 660460 599213 025157 204159 732032 774980 325041 885869 756212 437473 935040 > 4¹⁹⁷ [i]