MinT - Best Known (203−123, 203, s)-Nets in Base 4

Best Known (203−123, 203, s)-Nets in Base 4

(203−123, 203, 104)-Net over F₄ — Constructive and digital

Digital (80, 203, 104)-net over F₄, using

t-expansion [i] based on digital (73, 203, 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]

(203−123, 203, 112)-Net over F₄ — Digital

Digital (80, 203, 112)-net over F₄, using

t-expansion [i] based on digital (73, 203, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(203−123, 203, 724)-Net in Base 4 — Upper bound on s

There is no (80, 203, 725)-net in base 4, because

1 times m-reduction [i] would yield (80, 202, 725)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 337666 423230 535039 382499 885200 707228 910032 340630 271406 996496 629379 781655 803023 257618 694374 065894 925449 736238 692316 079200 > 4²⁰² [i]