MinT - Best Known (207−123, 207, s)-Nets in Base 4

Best Known (207−123, 207, s)-Nets in Base 4

(207−123, 207, 104)-Net over F₄ — Constructive and digital

Digital (84, 207, 104)-net over F₄, using

t-expansion [i] based on digital (73, 207, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(207−123, 207, 129)-Net over F₄ — Digital

Digital (84, 207, 129)-net over F₄, using

t-expansion [i] based on digital (81, 207, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(207−123, 207, 798)-Net in Base 4 — Upper bound on s

There is no (84, 207, 799)-net in base 4, because

1 times m-reduction [i] would yield (84, 206, 799)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10917 499551 677861 021128 671045 271026 574206 213526 335613 207979 158156 982321 997770 945694 956389 510458 678838 730743 590860 969351 129680 > 4²⁰⁶ [i]