MinT - Best Known (249−147, 249, s)-Nets in Base 4

Best Known (249−147, 249, s)-Nets in Base 4

(249−147, 249, 104)-Net over F₄ — Constructive and digital

Digital (102, 249, 104)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(249−147, 249, 144)-Net over F₄ — Digital

Digital (102, 249, 144)-net over F₄, using

t-expansion [i] based on digital (91, 249, 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]

(249−147, 249, 977)-Net in Base 4 — Upper bound on s

There is no (102, 249, 978)-net in base 4, because

1 times m-reduction [i] would yield (102, 248, 978)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214984 672264 630633 899117 210201 592439 191578 014255 448269 755978 572160 947179 647377 936358 048372 652465 376433 531850 986289 545186 624369 881686 390740 167949 274230 > 4²⁴⁸ [i]