MinT - Best Known (85, 85+98, s)-Nets in Base 4

Best Known (85, 85+98, s)-Nets in Base 4

(85, 85+98, 104)-Net over F₄ — Constructive and digital

Digital (85, 183, 104)-net over F₄, using

t-expansion [i] based on digital (73, 183, 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]

(85, 85+98, 129)-Net over F₄ — Digital

Digital (85, 183, 129)-net over F₄, using

t-expansion [i] based on digital (81, 183, 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]

(85, 85+98, 1089)-Net in Base 4 — Upper bound on s

There is no (85, 183, 1090)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 155 515267 719712 569480 804533 656162 075011 690110 503785 045193 347778 273145 153306 743085 938968 981269 428087 264537 650628 > 4¹⁸³ [i]