MinT - Best Known (197−91, 197, s)-Nets in Base 4

Best Known (197−91, 197, s)-Nets in Base 4

(197−91, 197, 130)-Net over F₄ — Constructive and digital

Digital (106, 197, 130)-net over F₄, using

t-expansion [i] based on digital (105, 197, 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]

(197−91, 197, 182)-Net over F₄ — Digital

Digital (106, 197, 182)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−91, 197, 2425)-Net in Base 4 — Upper bound on s

There is no (106, 197, 2426)-net in base 4, because

1 times m-reduction [i] would yield (106, 196, 2426)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10159 382113 438620 137309 059364 170487 602201 253506 591987 032078 024738 862947 959308 371611 553368 194638 914853 380288 423272 751140 > 4¹⁹⁶ [i]