MinT - Best Known (197−83, 197, s)-Nets in Base 4

Best Known (197−83, 197, s)-Nets in Base 4

(197−83, 197, 130)-Net over F₄ — Constructive and digital

Digital (114, 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]

(197−83, 197, 244)-Net over F₄ — Digital

Digital (114, 197, 244)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−83, 197, 4030)-Net in Base 4 — Upper bound on s

There is no (114, 197, 4031)-net in base 4, because

1 times m-reduction [i] would yield (114, 196, 4031)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10164 797461 186398 101482 585251 749026 221016 742493 509380 430038 309392 115609 660758 550196 490949 839585 904837 346977 601212 886794 > 4¹⁹⁶ [i]