MinT - Best Known (221−101, 221, s)-Nets in Base 4

Best Known (221−101, 221, s)-Nets in Base 4

(221−101, 221, 130)-Net over F₄ — Constructive and digital

Digital (120, 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]

(221−101, 221, 208)-Net over F₄ — Digital

Digital (120, 221, 208)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−101, 221, 2853)-Net in Base 4 — Upper bound on s

There is no (120, 221, 2854)-net in base 4, because

1 times m-reduction [i] would yield (120, 220, 2854)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 851010 217957 006240 485237 172382 758072 142020 401401 249655 152920 372199 921765 382844 452093 764590 542261 476081 557664 867817 633325 944701 116256 > 4²²⁰ [i]