MinT - Best Known (119, 119+125, s)-Nets in Base 4

Best Known (119, 119+125, s)-Nets in Base 4

(119, 119+125, 130)-Net over F₄ — Constructive and digital

Digital (119, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(119, 119+125, 168)-Net over F₄ — Digital

Digital (119, 244, 168)-net over F₄, using

t-expansion [i] based on digital (115, 244, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(119, 119+125, 1775)-Net in Base 4 — Upper bound on s

There is no (119, 244, 1776)-net in base 4, because

1 times m-reduction [i] would yield (119, 243, 1776)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 202 262148 864628 317199 101041 076876 219135 548656 977057 059633 782303 591075 160587 402081 263911 641329 750213 418312 547633 148233 434484 997944 562467 513366 214100 > 4²⁴³ [i]