MinT - Best Known (208−107, 208, s)-Nets in Base 4

Best Known (208−107, 208, s)-Nets in Base 4

(208−107, 208, 104)-Net over F₄ — Constructive and digital

Digital (101, 208, 104)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(208−107, 208, 144)-Net over F₄ — Digital

Digital (101, 208, 144)-net over F₄, using

t-expansion [i] based on digital (91, 208, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(208−107, 208, 1498)-Net in Base 4 — Upper bound on s

There is no (101, 208, 1499)-net in base 4, because

1 times m-reduction [i] would yield (101, 207, 1499)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42459 113640 924252 409932 532116 396823 840718 094593 415642 397690 070574 962133 879541 182758 822362 511567 650269 994881 704943 529300 380952 > 4²⁰⁷ [i]