MinT - Best Known (109, 109+91, s)-Nets in Base 4

Best Known (109, 109+91, s)-Nets in Base 4

(109, 109+91, 130)-Net over F₄ — Constructive and digital

Digital (109, 200, 130)-net over F₄, using

t-expansion [i] based on digital (105, 200, 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+91, 193)-Net over F₄ — Digital

Digital (109, 200, 193)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+91, 2664)-Net in Base 4 — Upper bound on s

There is no (109, 200, 2665)-net in base 4, because

1 times m-reduction [i] would yield (109, 199, 2665)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 656283 785022 717227 433276 415623 074560 026646 707354 005861 535658 589996 246763 146504 560352 840974 985543 648935 666190 969070 500992 > 4¹⁹⁹ [i]