MinT - Best Known (97, 97+125, s)-Nets in Base 4

Best Known (97, 97+125, s)-Nets in Base 4

(97, 97+125, 104)-Net over F₄ — Constructive and digital

Digital (97, 222, 104)-net over F₄, using

t-expansion [i] based on digital (73, 222, 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]

(97, 97+125, 144)-Net over F₄ — Digital

Digital (97, 222, 144)-net over F₄, using

t-expansion [i] based on digital (91, 222, 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]

(97, 97+125, 1066)-Net in Base 4 — Upper bound on s

There is no (97, 222, 1067)-net in base 4, because

1 times m-reduction [i] would yield (97, 221, 1067)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 748201 884560 297840 969689 391611 338914 570612 201011 755504 055121 637793 073898 053667 348570 396664 374195 666241 797579 162128 465369 615434 760960 > 4²²¹ [i]