MinT - Best Known (103, 103+136, s)-Nets in Base 4

Best Known (103, 103+136, s)-Nets in Base 4

(103, 103+136, 104)-Net over F₄ — Constructive and digital

Digital (103, 239, 104)-net over F₄, using

t-expansion [i] based on digital (73, 239, 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]

(103, 103+136, 144)-Net over F₄ — Digital

Digital (103, 239, 144)-net over F₄, using

t-expansion [i] based on digital (91, 239, 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]

(103, 103+136, 1083)-Net in Base 4 — Upper bound on s

There is no (103, 239, 1084)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 788731 606546 362271 402858 129820 358012 301988 479655 861681 688139 071542 328224 760686 872826 768929 981480 725500 324325 444505 789181 653320 079432 936663 807840 > 4²³⁹ [i]