MinT - Best Known (210−89, 210, s)-Nets in Base 4

Best Known (210−89, 210, s)-Nets in Base 4

(210−89, 210, 130)-Net over F₄ — Constructive and digital

Digital (121, 210, 130)-net over F₄, using

t-expansion [i] based on 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]

(210−89, 210, 254)-Net over F₄ — Digital

Digital (121, 210, 254)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−89, 210, 4128)-Net in Base 4 — Upper bound on s

There is no (121, 210, 4129)-net in base 4, because

1 times m-reduction [i] would yield (121, 209, 4129)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 679221 459766 208112 462002 649767 854141 341233 337896 108177 392554 140990 272681 532656 711204 991889 370944 243203 752520 046721 586800 313344 > 4²⁰⁹ [i]