MinT - Best Known (18, 18+48, s)-Nets in Base 81

Best Known (18, 18+48, s)-Nets in Base 81

(18, 18+48, 370)-Net over F₈₁ — Constructive and digital

Digital (18, 66, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 66, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(18, 18+48, 21695)-Net in Base 81 — Upper bound on s

There is no (18, 66, 21696)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 912500 035603 534733 002162 038116 610606 585041 367847 039896 857969 424054 967005 558437 262483 223886 161293 244075 529700 019064 200247 582721 > 81⁶⁶ [i]