MinT - Best Known (221−103, 221, s)-Nets in Base 4

Best Known (221−103, 221, s)-Nets in Base 4

(221−103, 221, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(221−103, 221, 196)-Net over F₄ — Digital

Digital (118, 221, 196)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−103, 221, 2575)-Net in Base 4 — Upper bound on s

There is no (118, 221, 2576)-net in base 4, because

1 times m-reduction [i] would yield (118, 220, 2576)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 863042 630691 020584 139307 524004 130407 065268 478425 217813 023847 620397 403414 483869 149272 000338 201180 155026 774622 949754 365507 137325 835360 > 4²²⁰ [i]