MinT - Best Known (221−105, 221, s)-Nets in Base 4

Best Known (221−105, 221, s)-Nets in Base 4

(221−105, 221, 130)-Net over F₄ — Constructive and digital

Digital (116, 221, 130)-net over F₄, using

t-expansion [i] based on digital (105, 221, 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]

(221−105, 221, 184)-Net over F₄ — Digital

Digital (116, 221, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−105, 221, 2334)-Net in Base 4 — Upper bound on s

There is no (116, 221, 2335)-net in base 4, because

1 times m-reduction [i] would yield (116, 220, 2335)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 899432 546693 754028 751492 886258 871770 988034 504350 393340 435362 746777 149240 021873 066582 609155 151326 198598 624640 214853 584235 605675 791320 > 4²²⁰ [i]