MinT - Best Known (208−117, 208, s)-Nets in Base 4

Best Known (208−117, 208, s)-Nets in Base 4

(208−117, 208, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(208−117, 208, 144)-Net over F₄ — Digital

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]

(208−117, 208, 1006)-Net in Base 4 — Upper bound on s

There is no (91, 208, 1007)-net in base 4, because

1 times m-reduction [i] would yield (91, 207, 1007)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42380 739978 156046 827887 561601 651358 951141 247996 309820 529151 752830 131842 533616 816901 419835 436836 032143 119925 967423 808247 791356 > 4²⁰⁷ [i]