MinT - Best Known (119, 119+121, s)-Nets in Base 4

Best Known (119, 119+121, s)-Nets in Base 4

(119, 119+121, 130)-Net over F₄ — Constructive and digital

Digital (119, 240, 130)-net over F₄, using

t-expansion [i] based on digital (105, 240, 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+121, 168)-Net over F₄ — Digital

Digital (119, 240, 168)-net over F₄, using

t-expansion [i] based on digital (115, 240, 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+121, 1884)-Net in Base 4 — Upper bound on s

There is no (119, 240, 1885)-net in base 4, because

1 times m-reduction [i] would yield (119, 239, 1885)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 784854 972911 420276 077263 421663 309070 944177 468975 338335 534576 946121 306790 260706 058714 493767 877189 325709 379503 991958 152672 607525 510661 416446 904290 > 4²³⁹ [i]