MinT - Best Known (119, 119+129, s)-Nets in Base 4

Best Known (119, 119+129, s)-Nets in Base 4

(119, 119+129, 130)-Net over F₄ — Constructive and digital

Digital (119, 248, 130)-net over F₄, using

t-expansion [i] based on digital (105, 248, 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+129, 168)-Net over F₄ — Digital

Digital (119, 248, 168)-net over F₄, using

t-expansion [i] based on digital (115, 248, 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+129, 1680)-Net in Base 4 — Upper bound on s

There is no (119, 248, 1681)-net in base 4, because

1 times m-reduction [i] would yield (119, 247, 1681)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52372 899663 422463 304463 339904 795718 917093 420259 194570 854262 950911 101731 866985 957065 982665 681510 388016 619990 229546 235963 940876 644903 399201 588771 783670 > 4²⁴⁷ [i]