MinT - Best Known (234−119, 234, s)-Nets in Base 4

Best Known (234−119, 234, s)-Nets in Base 4

(234−119, 234, 130)-Net over F₄ — Constructive and digital

Digital (115, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(234−119, 234, 168)-Net over F₄ — Digital

Digital (115, 234, 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]

(234−119, 234, 1766)-Net in Base 4 — Upper bound on s

There is no (115, 234, 1767)-net in base 4, because

1 times m-reduction [i] would yield (115, 233, 1767)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 192 451642 788263 740467 013573 054734 235123 725457 916273 744603 238158 580219 286802 653576 154981 177635 250002 433952 416488 914347 512423 919846 115363 356992 > 4²³³ [i]