MinT - Best Known (83, 83+158, s)-Nets in Base 4

Best Known (83, 83+158, s)-Nets in Base 4

(83, 83+158, 104)-Net over F₄ — Constructive and digital

Digital (83, 241, 104)-net over F₄, using

t-expansion [i] based on digital (73, 241, 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]

(83, 83+158, 129)-Net over F₄ — Digital

Digital (83, 241, 129)-net over F₄, using

t-expansion [i] based on digital (81, 241, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(83, 83+158, 628)-Net in Base 4 — Upper bound on s

There is no (83, 241, 629)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 997148 240016 900151 535444 094152 448817 270578 943697 660613 573704 719148 384082 351447 035361 094136 255656 841748 774935 855838 667467 074153 127136 678030 305616 > 4²⁴¹ [i]