MinT - Best Known (154, 154+66, s)-Nets in Base 3

Best Known (154, 154+66, s)-Nets in Base 3

(154, 154+66, 246)-Net over F₃ — Constructive and digital

Digital (154, 220, 246)-net over F₃, using

3¹ times duplication [i] based on digital (153, 219, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 73, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(154, 154+66, 481)-Net over F₃ — Digital

Digital (154, 220, 481)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+66, 9947)-Net in Base 3 — Upper bound on s

There is no (154, 220, 9948)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 927 399068 887657 040874 564712 913075 354220 574589 057809 386369 684950 911319 534373 787623 307082 997681 826082 605497 > 3²²⁰ [i]