MinT - Best Known (216−128, 216, s)-Nets in Base 4

Best Known (216−128, 216, s)-Nets in Base 4

(216−128, 216, 104)-Net over F₄ — Constructive and digital

Digital (88, 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]

(216−128, 216, 129)-Net over F₄ — Digital

Digital (88, 216, 129)-net over F₄, using

t-expansion [i] based on digital (81, 216, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(216−128, 216, 833)-Net in Base 4 — Upper bound on s

There is no (88, 216, 834)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11419 022374 735823 533227 031288 606558 082138 827910 823837 904154 877959 966028 275493 704636 850356 096922 526781 822639 092475 460823 416874 980805 > 4²¹⁶ [i]