MinT - Best Known (147, 147+72, s)-Nets in Base 4

Best Known (147, 147+72, s)-Nets in Base 4

(147, 147+72, 240)-Net over F₄ — Constructive and digital

Digital (147, 219, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 73, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(147, 147+72, 626)-Net over F₄ — Digital

Digital (147, 219, 626)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+72, 21855)-Net in Base 4 — Upper bound on s

There is no (147, 219, 21856)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 710316 914982 931342 750993 020943 846655 365389 968283 696766 899022 724605 737893 771742 236421 056369 235608 065206 134998 826059 939503 869227 099810 > 4²¹⁹ [i]