MinT - Best Known (216−114, 216, s)-Nets in Base 4

Best Known (216−114, 216, s)-Nets in Base 4

(216−114, 216, 104)-Net over F₄ — Constructive and digital

Digital (102, 216, 104)-net over F₄, using

t-expansion [i] based on digital (73, 216, 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]

(216−114, 216, 144)-Net over F₄ — Digital

Digital (102, 216, 144)-net over F₄, using

t-expansion [i] based on digital (91, 216, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(216−114, 216, 1360)-Net in Base 4 — Upper bound on s

There is no (102, 216, 1361)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11172 537317 786531 340470 929278 014618 002281 808780 705734 254963 150915 910386 099210 658328 538400 299715 610099 302688 546014 043521 473114 374240 > 4²¹⁶ [i]