MinT - Best Known (209−93, 209, s)-Nets in Base 4

Best Known (209−93, 209, s)-Nets in Base 4

(209−93, 209, 130)-Net over F₄ — Constructive and digital

Digital (116, 209, 130)-net over F₄, using

t-expansion [i] based on digital (105, 209, 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]

(209−93, 209, 216)-Net over F₄ — Digital

Digital (116, 209, 216)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−93, 209, 3128)-Net in Base 4 — Upper bound on s

There is no (116, 209, 3129)-net in base 4, because

1 times m-reduction [i] would yield (116, 208, 3129)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 171665 335512 267369 396043 135941 258562 894882 094250 282355 353644 333578 079920 157480 259384 049792 571593 163321 839246 904418 241278 261592 > 4²⁰⁸ [i]