MinT - Best Known (210−105, 210, s)-Nets in Base 4

Best Known (210−105, 210, s)-Nets in Base 4

(210−105, 210, 130)-Net over F₄ — Constructive and digital

Digital (105, 210, 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]

(210−105, 210, 150)-Net over F₄ — Digital

Digital (105, 210, 150)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−105, 210, 1730)-Net in Base 4 — Upper bound on s

There is no (105, 210, 1731)-net in base 4, because

1 times m-reduction [i] would yield (105, 209, 1731)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 695261 207154 208425 850263 267197 436239 577769 218422 400101 409248 934831 093730 110649 361113 731072 563385 646297 009350 495501 315594 372496 > 4²⁰⁹ [i]