MinT - Best Known (124, 221, s)-Nets in Base 4

Best Known (124, 221, s)-Nets in Base 4

(124, 221, 130)-Net over F₄ — Constructive and digital

Digital (124, 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]

(124, 221, 237)-Net over F₄ — Digital

Digital (124, 221, 237)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 221, 3550)-Net in Base 4 — Upper bound on s

There is no (124, 221, 3551)-net in base 4, because

1 times m-reduction [i] would yield (124, 220, 3551)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 847003 099143 803465 771481 993176 473808 241151 608304 900206 220694 207608 482627 420073 177239 048677 233806 054282 271956 722351 574420 631996 453250 > 4²²⁰ [i]