MinT - Best Known (100, 100+88, s)-Nets in Base 4

Best Known (100, 100+88, s)-Nets in Base 4

(100, 100+88, 130)-Net over F₄ — Constructive and digital

Digital (100, 188, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 94, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(100, 100+88, 168)-Net over F₄ — Digital

Digital (100, 188, 168)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+88, 2113)-Net in Base 4 — Upper bound on s

There is no (100, 188, 2114)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 156839 892169 753368 972248 286347 511085 498729 952277 281856 908285 157254 169425 746615 015871 806238 403497 325683 833801 057840 > 4¹⁸⁸ [i]