MinT - Best Known (128−54, 128, s)-Nets in Base 16

Best Known (128−54, 128, s)-Nets in Base 16

(128−54, 128, 534)-Net over F₁₆ — Constructive and digital

Digital (74, 128, 534)-net over F₁₆, using

trace code for nets [i] based on digital (10, 64, 267)-net over F₂₅₆, using
- net from sequence [i] based on digital (10, 266)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(128−54, 128, 1138)-Net over F₁₆ — Digital

Digital (74, 128, 1138)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−54, 128, 372150)-Net in Base 16 — Upper bound on s

There is no (74, 128, 372151)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13408 051058 584558 809075 036531 052863 028706 448768 947556 968988 172082 369701 596369 880319 562566 302730 785620 426726 113840 851454 923875 555927 860082 248501 588792 538256 > 16¹²⁸ [i]